Thin shell analysis from scattered points with maximum-entropy approximants

Author (s): Millán, D; Rosolen, A and Arroyo, M.
Journal: International Journal for Numerical Methods in Engineering

Volume: 85, Iss. 6
Pages: 723 – 751
Date: 2011

Abstract:
We present a method to process embedded smooth manifolds using sets of points alone. This method avoids any global parameterization and hence is applicable to surfaces of any genus. It combines three ingredients: (1) the automatic detection of the local geometric structure of the manifold by statistical learning methods, (2) the local parameterization of the surface using smooth meshfree (here maximum-entropy) approximants, and (3) patching together the local representations by means of a partition of unity. Mesh-based methods can deal with surfaces of complex topology, since they rely on the element-level parameterizations, but cannot handle high-dimensional manifolds, while previous meshfree methods for thin shells consider a global parametric domain, which seriously limits the kinds of surfaces that can be treated. We present the implementation of the method in the context of Kirchhoff-Love shells, but it is applicable to other calculations on manifolds in any dimension. With the smooth approximants, this fourth-order partial differential equation is treated directly. We show the good performance of the method on the basis of the classical obstacle course. Additional calculations exemplify the exibility of the proposed approach in treating surfaces of complex topology and geometry.

Journal paper (from the publisher)  
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Bibtex:

@article {NME:NME2992,
author = {Millán, D. and Rosolen, A. and Arroyo, M.},
title = {Thin shell analysis from scattered points with maximum-entropy approximants},
journal = {International Journal for Numerical Methods in Engineering},
volume = {85},
number = {6},
pages = {723--751},
issn = {1097-0207},
url = {http://dx.doi.org/10.1002/nme.2992},
doi = {10.1002/nme.2992},
year = {2011},
}